{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# 2D Optimal transport between empirical distributions\n",
    "\n",
    "\n",
    "Illustration of 2D optimal transport between discributions that are weighted\n",
    "sum of diracs. The OT matrix is plotted with the samples.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Author: Remi Flamary <remi.flamary@unice.fr>\n",
    "#         Kilian Fatras <kilian.fatras@irisa.fr>\n",
    "#\n",
    "# License: MIT License\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pylab as pl\n",
    "import ot\n",
    "import ot.plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate data\n",
    "-------------\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#%% parameters and data generation\n",
    "\n",
    "n = 50  # nb samples\n",
    "\n",
    "mu_s = np.array([0, 0])\n",
    "cov_s = np.array([[1, 0], [0, 1]])\n",
    "\n",
    "mu_t = np.array([4, 4])\n",
    "cov_t = np.array([[1, -.8], [-.8, 1]])\n",
    "\n",
    "xs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s)\n",
    "xt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t)\n",
    "\n",
    "a, b = np.ones((n,)) / n, np.ones((n,)) / n  # uniform distribution on samples\n",
    "\n",
    "# loss matrix\n",
    "M = ot.dist(xs, xt)\n",
    "M /= M.max()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot data\n",
    "---------\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Cost matrix M')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%% plot samples\n",
    "\n",
    "pl.figure(1)\n",
    "pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\n",
    "pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\n",
    "pl.legend(loc=0)\n",
    "pl.title('Source and target distributions')\n",
    "\n",
    "pl.figure(2)\n",
    "pl.imshow(M, interpolation='nearest')\n",
    "pl.title('Cost matrix M')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute EMD\n",
    "-----------\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'OT matrix with samples')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%% EMD\n",
    "\n",
    "G0 = ot.emd(a, b, M)\n",
    "\n",
    "pl.figure(3)\n",
    "pl.imshow(G0, interpolation='nearest')\n",
    "pl.title('OT matrix G0')\n",
    "\n",
    "pl.figure(4)\n",
    "ot.plot.plot2D_samples_mat(xs, xt, G0, c=[.5, .5, 1])\n",
    "pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\n",
    "pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\n",
    "pl.legend(loc=0)\n",
    "pl.title('OT matrix with samples')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute Sinkhorn\n",
    "----------------\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%% sinkhorn\n",
    "\n",
    "# reg term\n",
    "lambd = 1e-3\n",
    "\n",
    "Gs = ot.sinkhorn(a, b, M, lambd)\n",
    "\n",
    "pl.figure(5)\n",
    "pl.imshow(Gs, interpolation='nearest')\n",
    "pl.title('OT matrix sinkhorn')\n",
    "\n",
    "pl.figure(6)\n",
    "ot.plot.plot2D_samples_mat(xs, xt, Gs, color=[.5, .5, 1])\n",
    "pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\n",
    "pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\n",
    "pl.legend(loc=0)\n",
    "pl.title('OT matrix Sinkhorn with samples')\n",
    "\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Emprirical Sinkhorn\n",
    "----------------\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: numerical errors at iteration 0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/rflamary/PYTHON/POT/ot/bregman.py:374: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  v = np.divide(b, KtransposeU)\n",
      "/home/rflamary/PYTHON/POT/ot/plot.py:83: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  if G[i, j] / mx > thr:\n"
     ]
    },
    {
     "data": {
      "image/png": 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/okIJfkSFEvyICiX4ERVK8CMqlOBHVCjBj6hQgh9RoQQ/okIJfkSFEvyICiX4ERVK8CMqlOBHVCjBj6iQbI/fwqSHgPuA/YGHx23BYzOZaoXJVe9kqhUmR70H2z5gpE7jGvxfLVRab3vxuC94FCZTrTC56p1MtcLkq3c4OdWPqFCCH1GhiQr+8gla7mhMplphctU7mWqFyVfvkCbkGj8iJlZO9SMqlOBHVGhcgy9piaQ7JG2UdPZ4Lrsdki6RtFXSrS1tsyWtknRX+fvsiayxn6SDJK2RdLuk2ySdUdp7td4Zkq6X9INS77ml/RBJ68p3YqWkaRNdaz9JUyTdJOnaMt6zte6pcQu+pCnAPwPHAYuAN0paNF7Lb9OlwJIBbWcDq20fCqwu471gN3Cm7UXAkcDby/bs1Xp3AkfbfjFwOLBE0pHAecAnbC8EHgVOm8AaBzoD2NAy3su17pHxPOIfAWy0fY/tJ4DLgBPHcfkjsv1t4JEBzScCK8rwCuCkcS1qCLa32P5+Gd5B8wWdR+/Wa9uPldGp5WXgaODK0t4z9UqaD7wauKiMix6tdTTGM/jzgE0t45tLW6+bY3tLGX4AmDORxQxG0gLgJcA6erjecup8M7AVWAXcDWyzvbt06aXvxCeBs4Cnyvh+9G6teyw39/aAm98+e+r3T0kzgauAd9ne3jqt1+q1/aTtw4H5NGeAL5jgkgYl6QRgq+0bJ7qWbukbx2XdDxzUMj6/tPW6ByXNtb1F0lyao1VPkDSVJvRfsv3V0tyz9fazvU3SGuAVwCxJfeVI2ivfiVcCr5V0PDAD2Be4gN6sdVTG84h/A3BouTM6DTgFuGYclz9a1wBLy/BS4OoJrOVXyjXnxcAG2x9vmdSr9R4gaVYZ3gs4lua+xBrgdaVbT9Rr+/2259teQPM9/ZbtU+nBWkfN9ri9gOOBO2mu7T44nstus76vAFuAXTTXcKfRXNutBu4C/hOYPdF1llp/j+Y0/hbg5vI6vofr/W3gplLvrcCHSvtzgeuBjcAVwPSJrnVA3UcB106GWvfklUd2IyqUm3sRFUrwIyqU4EdUKMGPqFCCH1GhBD+iQgl+RIX+D3hVA73ajSqrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%% sinkhorn\n",
    "\n",
    "# reg term\n",
    "lambd = 1e-3\n",
    "\n",
    "Ges = ot.bregman.empirical_sinkhorn(xs, xt, lambd)\n",
    "\n",
    "pl.figure(7)\n",
    "pl.imshow(Ges, interpolation='nearest')\n",
    "pl.title('OT matrix empirical sinkhorn')\n",
    "\n",
    "pl.figure(8)\n",
    "ot.plot.plot2D_samples_mat(xs, xt, Ges, color=[.5, .5, 1])\n",
    "pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\n",
    "pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\n",
    "pl.legend(loc=0)\n",
    "pl.title('OT matrix Sinkhorn from samples')\n",
    "\n",
    "pl.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
